
Algorithm REF  is an extension of the forward-backward-forward splitting method in [1]} which is in the deterministic setting. In the setting of this method, we do not need the cocoercive condition as in [2]}, [3]}, [4]}.

When \(\alpha _n=0\) , Algorithm REF  reduces to (3.2) in [5]}. However, the conditions for the convergences are different from that in [5]}.

In [7]}, [8]}, for solving (REF ), the authors designed stochastic forward-backward-forward splitting methods which require a large number of samples in each iteration. Our results are also different from that in [7]}, [8]}.

Evidently, we have from (REF ) that
\(\alpha _n\Vert x_n-x_{n-1}\Vert \le \epsilon _n.\) 


